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The dark matter enclosed in a density perturbation with a large initialamplitude (delta-rho/rho > 1e-3) collapses shortly after recombination andforms an ultracompact minihalo (UCMH). Their high central densities make UCMHsespecially suitable for detection via astrometric microlensing: as the UCMHmoves, it changes the apparent position of background stars. A UCMH with a masslarger than a few solar masses can produce a distinctive astrometricmicrolensing signal that is detectable by the space astrometry mission Gaia. IfGaia does not detect gravitational lensing by any UCMHs, then it establishes anupper limit on their abundance and constrains the amplitude of the primordialpower spectrum for k~2700 Mpc^{-1}. These constraints complement the upperbound on the amplitude of the primordial power spectrum derived from limits ongamma-ray emission from UCMHs because the astrometric microlensing signalproduced by an UCMH is maximized if the dark-matter annihilation rate is toolow to affect the UCMH's density profile. If dark matter annihilation withinUCMHs is not detectable, a search for UCMHs by Gaia could constrain theamplitude of the primordial power spectrum to be less than 1e-5; this bound isthree orders of magnitude stronger than the bound derived from the absence ofprimordial black holes.

A new probe of the small-scale primordial power spectrum: astrometric microlensing by ultracompact minihalos